#include <Eigen/Dense>
#include <iostream>

using namespace std;
using namespace Eigen;

int
main()
{
	Matrix2f A, b;
	LLT<Matrix2f> llt;
	A << 2, -1, -1, 3;
	b << 1, 2, 3, 1;
	cout << "Here is the matrix A:\n" << A << endl;
	cout << "Here is the right hand side b:\n" << b << endl;
	cout << "Computing LLT decomposition..." << endl;
	llt.compute(A);
	cout << "The solution is:\n" << llt.solve(b) << endl;
	A(1, 1)++;
	cout << "The matrix A is now:\n" << A << endl;
	cout << "Computing LLT decomposition..." << endl;
	llt.compute(A);
	cout << "The solution is now:\n" << llt.solve(b) << endl;
}
